Cylindrical Algebraic Decomposition in the RegularChains Library

  • Changbo Chen
  • Marc Moreno Maza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry and has been implemented in several software. While existing implementations are all based on Collins’ projection-lifting scheme and its subsequent ameliorations, the implementation of CAD in the RegularChains library is based on triangular decomposition of polynomial systems and real root isolation of regular chains. The function in the RegularChains library for computing CAD is called CylindricalAlgebraicDecompose. In this paper, we illustrate by examples the functionality, the underlying theory and algorithm, as well the implementation techniques of CylindricalAlgebraicDecompose. An application of it is also provided.

Keywords

Cylindrical algebraic decomposition triangular decomposition RegularChains 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Changbo Chen
    • 1
  • Marc Moreno Maza
    • 2
  1. 1.Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent TechnologyChinese Academy of SciencesChina
  2. 2.ORCCAUniversity of Western OntarioCanada

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